I’m not fully sure of my answer, its a long shot with the ‘answers’ to all three -fixes being quite far-fetched but here is my attempt:
You are
a MUSTANG
My prefix tells you fate has come.
MUST - Refers to fate being inevitable, it is a must for it to come.
My suffix is the pain in the past.
STANG - Past tense of sting, so it is the past pain from a sting. (“Stang” is obsolete, so I’m quite uncertain)
My infix is from the burning sun.
STAN - Slang for a very overzealous fan, one who has a burning passion for his/her idol, so the ‘burning passion’ comes from the burning sun.
My whole is American and fast.
MUSTANG - Ford Mustang, series of fast American cars.